Question

The current age of the father is three times the age of the son, 5 years ago the age of the father was four times the age of the son, what is the age of the son?​

Answer 1

Given :

• The current age of the father is three times the age of the son, 5 years ago the age of the father was four times the age of the son.

To Find :

• present age of son = ?

Solution :

Let the present age of son be 'x' and father be '3x'.

★ 5 years ago :

• Age of son = x - 5 years
• Age of father = 3x - 5 years

⚽ According to Question now :

→ 3x - 5 = 4(x - 5)

→ 3x - 5 = 4x - 20

Combining the like terms we get :

→ -5 + 20 = 4x - 3x

→ 15 = x

→ x = 15 years

• Hence,the present age of son will be 15 years.

★ Points to Remember :

• If the present age is x, then y times the present age = yx.
• If the present age is x, then age y years later/hence = x + y.
• If the present age is x, then age y years ago = x – y.

Answer 2

Given:-

• At present the age of Father is 3 times the age of his son.
• Five years ago the Father was 4 times that age of his son.

Find:-

• Present age of his son.

Solution:-

Let, The present age of son be ❝x❞ yrs

⛂ The father is three times the age of his son.

So, Father's is ❝3x❞

⛀ Five years ago:

➱ Age of Son = x - 5 yrs

➱ Age of Father = 3x - 5 yrs

According To Question

⛂ Five years ago age of Father is four times the age of son.

➠ 3x - 5 = 4(x - 5)

➠ 3x - 5 = 4x - 20

➠ 3x - 4x = -20 + 5

➠ - x = -15

➠ x = 15..........[∵ - = - ⇛ + ]

So, x = 15

$\qquad$ _______________________

➮ Present Age of Son = x = 15yrs

Hence,

❏ Present age of Sone = 15yrs

$\qquad$ _______________________

Let's Verify It!

For verifying we simply put the value of x in the eq.

❍ 3x - 5 = 4(x - 5)

❍ 3(15) - 5 = 4(15 - 5)

❍ 45 - 5 = 4(10)

❍ 40 = 40

✯ L.H.S = R.H.S ✯

✠ Hence, Verified ✠